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Ch.5 - Thermochemistry
All textbooksBrown 14th EditionCh.5 - ThermochemistryProblem 102b
Chapter 5, Problem 102b

A sample of gas is contained in a cylinder-and-piston arrangement. There is an external pressure of 100 kPa. The gas undergoes the change in state shown in the drawing. (b) Now assume that the cylinder and piston are made up of a thermal conductor such as a metal. During the state change, the cylinder gets colder to the touch. What is the sign of q for the state change in this case? Describe the difference in the state of the system at the end of the process in the two cases. What can you say about the relative values of E?

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insert step 1: Understand the problem context. The gas is in a cylinder with a piston, and there is an external pressure of 100 kPa. The cylinder is made of a thermal conductor, and it gets colder during the state change.
insert step 2: Determine the sign of q (heat transfer). Since the cylinder gets colder, heat is being transferred from the system to the surroundings. Therefore, q is negative.
insert step 3: Compare the state of the system at the end of the process in both cases. In the first case, without the thermal conductor, the system might not lose as much heat to the surroundings. In the second case, with the thermal conductor, the system loses more heat, resulting in a lower internal energy.
insert step 4: Discuss the relative values of E (internal energy). In the case with the thermal conductor, the internal energy of the system decreases more compared to the case without the conductor, due to the greater heat loss.
insert step 5: Summarize the findings. The sign of q is negative, indicating heat loss. The system's internal energy is lower in the case with the thermal conductor due to increased heat transfer to the surroundings.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Thermodynamics and Heat Transfer

Thermodynamics is the study of energy transformations, particularly heat and work. In this context, heat transfer (q) refers to the energy exchanged between the system (the gas) and its surroundings. If the cylinder feels colder, it indicates that the gas is losing heat to the surroundings, resulting in a negative value for q, as energy is leaving the system.
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First Law of Thermodynamics

State Functions and Internal Energy (E)

State functions are properties that depend only on the current state of a system, not on how it got there. Internal energy (E) is a key state function representing the total energy contained within a system. During the gas's state change, if heat is lost (negative q), the internal energy of the gas decreases, which can be inferred from the first law of thermodynamics, stating that the change in internal energy is equal to heat added to the system minus work done by the system.
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Pressure-Volume Work

Pressure-volume work occurs when a gas expands or contracts against an external pressure. In this scenario, the external pressure is 100 kPa, and the gas's state change may involve work being done on or by the gas. Understanding how work interacts with heat transfer is crucial for analyzing the overall energy changes in the system, particularly in determining the relative values of internal energy before and after the process.
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Related Practice
Textbook Question

The automobile fuel called E85 consists of 85% ethanol and 15% gasoline. E85 can be used in the so-called flex-fuel vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of C8H18), that the average heat of combustion of C8H18(l) is 5400 kJ/mol, and that gasoline has an average density of 0.70 g/mL. The density of ethanol is 0.79 g/mL. (a) By using the information given as well as data in Appendix C, compare the energy produced by combustion of 1.0 L of gasoline and of 1.0 L of ethanol.

Textbook Question

The air bags that provide protection in automobiles in the event of an accident expand because of a rapid chemical reaction. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of q and w in this process?

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Textbook Question

Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not?

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Textbook Question

A house is designed to have passive solar energy features. Brickwork incorporated into the interior of the house acts as a heat absorber. Each brick weighs approximately 1.8 kg. The specific heat of the brick is 0.85 J/g•K. How many bricks must be incorporated into the interior of the house to provide the same total heat capacity as 1.7⨉103 gal of water?